Question

Two bodies of masses m and 4m are placed at a distance of r. Calculate the gravitational potential at a point on the line joining them where the gravitational field is zero.

Answer 1

Let the point be the position when the gravitational field is zero.,

`("Gm")/"x"^2 = ("G"(4"m"))/("r" - "x")^2`

`1/"x"^2 = 4/("r" - "x")^2`

Square root on both sides,

`1/"x" = 2/(("r" - "x"))`

∴ x = `"r"/3`

The point P is at a distance `"r"/3` from mass ‘m’ and `"2r"/3` from mass ‘4m’

Gravitational potential V = `(-"Gm")/(("r"/3)) - ("G"(4"m"))/(("2r"/3))`

= `(-3"Gm")/4 - (3"G"(4"m"))/(2"r")`

= `(-3"Gm")/"r" - (12"Gm")/(2"r")`

V = `(-9"Gm")/"r"`